Method and device for coding a digital hologram sequence

ABSTRACT

Disclosed is a method and a device for coding a sequence including first and second digital holograms representing respective scenes, the digital holograms being represented by a set of wavelets each defined by a multiplet of coordinates in multidimensional space. The first and second holograms are represented by first and second coefficients respectively associated with wavelets. The coding method includes the following steps: for each second coefficient, determining a remainder by a difference between the second coefficient concerned, associated with a first wavelet defined by a given multiplet, and the first coefficient) associated with a second wavelet defined by a multiplet having as its image the multiplet by a transform in the multidimenisonal space; coding the determined remainders. The transform is determined by analysis of variation between the first scene represented by the first digital hologram and the second scene represented by the second digital hologram.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to the technical field of digitalholography.

More particularly, it relates to a method and a device for encoding adigital hologram sequence.

Description of the Related Art

It has already been proposed, for example in the article “View-dependentcompression of digital hologram based on matching pursuit”, by Anas ElRhammad, Patrick Gioia, Antonin Gilles, Marco Cagnazzo and BeatricePesquet-Popescu in Optics, Photonics, and Digital Technologies forImaging Applications V. International Society for Optics and Photonics,2018, vol. 10679, p. 106790L, to represent a digital hologram by meansof a set of wavelets (for example Gabor wavelets).

Each wavelet is defined by several parameters characteristic of thewavelet concerned. The digital hologram is then represented by a set ofcoefficients respectively associated with the different wavelets.

The digital hologram can thus be easily reconstructed by summing thedifferent wavelets, each time weighted by the associated coefficient.

SUMMARY OF THE INVENTION

In this context, the present invention proposes a method for encoding asequence comprising at least a first digital hologram representing afirst scene and a second digital hologram representing a second scene,the first digital hologram and the second digital hologram beingrepresented by means of a set of wavelets each defined by a multiplet ofcoordinates in a multidimensional space,

the first hologram being represented by a set of first coefficientsrespectively associated with certain at least of the wavelets of saidset of wavelets and the second hologram being represented by a set ofsecond coefficients respectively associated with certain at least of thewavelets of said set of wavelets,

the encoding method comprising the following steps:

-   -   for each of a plurality of second coefficients, determining a        residual by difference between the second coefficient concerned,        associated with a first wavelet defined by a given multiplet,        and the first coefficient associated with a second wavelet        defined by a multiplet having for image the given multiplet by a        transform in the multidimensional space;    -   encoding the determined residuals,

wherein the transform is determined by analysis of variation between thefirst scene represented by the first digital hologram and the secondscene represented by the second digital hologram.

The transform makes it possible to assign certain at least of the firstcoefficients to wavelets other than those to which these firstcoefficients are assigned in the first hologram.

This transform thus makes it possible to construct (at least in part) apredicted hologram, which can be subtracted from the second hologram(coefficient by coefficient) in order to obtain residuals of lowervalue, whose encoding is more efficient.

Moreover, due to the fact that the transform is determined by analysisof variation between the first scene represented by the first digitalhologram and the second scene represented by the second digitalhologram, the predicted hologram will be as close as possible to thesecond hologram. This variation can correspond in practice to themovement of an object between the first scene and the second scene.

It can further be provided, for at least one second coefficient outsideof said plurality of second coefficients, a step of determining aresidual by difference between this second coefficient, associated witha third wavelet defined by another given multiplet, and the firstcoefficient associated with a fourth wavelet defined by anothermultiplet having for image the other given multiplet by anothertransform in the multidimensional space.

Another transform is thus used for other second coefficients, whichmakes it possible to refine the prediction of the second hologram bymeans of the first hologram.

This other transform is for example determined by analysis of anothervariation between the first scene and the second scene. This othervariation can correspond in practice to the movement of another object(different from the above-mentioned object) between the first scene andthe second scene.

The encoding method can moreover comprise the following steps:

-   -   distributing a part at least of the wavelets into different        groups of wavelets respectively associated with different parts        of the first scene or the second scene;    -   determining a transform of the multidimensional space for each        group of wavelets;    -   for each of the second coefficients of a given group of        wavelets, determining a residual by difference between the        second coefficient concerned, associated with a fifth wavelet        defined by a given multiplet, and the first coefficient        associated with a sixth wavelet defined by a multiplet having        for image this given multiplet by the transform associated with        the given group of wavelets.

The above-mentioned transform can be determined in practice as afunction of a movement, between the first scene and the second scene, ofa set of connected points (set of points called “connected component” inthe following description).

The transform can be determined, for example, on the basis ofthree-dimensional representations of the first scene and of the secondscene.

According to another possible embodiment, the encoding method cancomprise the following steps:

-   -   constructing a first depth map by means of the first digital        hologram;    -   constructing a second depth map by means of the second digital        hologram;    -   determining the transform on the basis of the first depth map        and the second depth map.

According to a possible embodiment, the depth being defined in a givendirection (here, a given direction of the three-dimensional spacecontaining the scene represented by the first digital hologram), thestep of constructing the first depth map (and/or the step ofconstructing the second depth map) can comprise the following steps:

-   -   reconstructing, by means of the first digital hologram (or,        depending on the case, by means of the second digital hologram),        the light field at a plurality of points;    -   for each of a plurality of depths, segmenting the points        associated with the depth concerned into a plurality of        segments, and determining values of a sharpness metric        respectively associated with said segments on the basis of the        light field reconstructed on the segment concerned;    -   for each element of the first (or second, depending on the case)        depth map, determining the depth for which the sharpness metric        is maximum among a set of segments aligned along said given        direction and respectively associated with the different depths        of the plurality of depths (the so-determined depth can thus be        associated with the element concerned of the first depth map or,        depending on the case, of the second depth map).

As described hereinafter, the coordinates of said multidimensional spacecan represent respectively a parameter representative of a first spatialcoordinate in the plane of the hologram, a parameter representative of asecond spatial coordinate in the plane of the hologram, a spatialfrequency dilation parameter and an orientation parameter.

The invention also proposes a device for encoding a sequence comprisingat least a first digital hologram representing a first scene and asecond digital hologram representing a second scene, the first digitalhologram and the second digital hologram being represented by means of aset of wavelets each defined by a multiplet of coordinates in amultidimensional space, the encoding device comprising:

-   -   a unit for storing a set of first coefficients, respectively        associated with certain at least of the wavelets of said set of        wavelets, and a set of second coefficients, respectively        associated with certain at least of the wavelets of said set of        wavelets, the set of first coefficients representing the first        digital hologram and the set of second coefficients representing        the second digital hologram;    -   a unit for determining, for each of a plurality of second        coefficients, a residual by difference between the second        coefficient concerned, associated with a first wavelet defined        by a given multiplet, and the first coefficient associated with        a second wavelet defined by a multiplet having for image the        given multiplet by transform in the multidimensional space;    -   a unit for encoding the determined residuals,

wherein the determination unit is designed to determine the transform byanalysis of variation between the first scene represented by the firstdigital hologram and the second scene represented by the second digitalhologram.

The determination unit and the encoding unit can for example beimplemented in practice by means of a processor of the encoding device,this processor being programmed (for example, by means of computerprogram instructions stored in a memory of the encoding device) toimplement respectively the steps of determining the residuals and thestep of encoding the residuals.

The invention moreover proposes, independently, a method fordistributing coefficients respectively associated with wavelets into aplurality of sets of coefficients, the coefficients associated with thewavelets representing a digital hologram intended to reproduce a scenecomprising a plurality of parts, the method comprising the followingsteps implemented for each of a plurality of said coefficients:

-   -   determining a straight line corresponding to the light ray        represented by the wavelet associated with the coefficient        concerned;    -   assigning the coefficient concerned to a set associated with the        part of the scene passed through by the determined straight        line.

When each wavelet is defined by a multiplet of coordinates in amultidimensional space, the straight line can be determined using thecoordinates of this multiplet.

For example, when these coordinates (defining the wavelet) comprise afirst spatial coordinate in the plane of the hologram, a second spatialcoordinate in the plane of the hologram, a spatial frequency dilationparameter and an orientation parameter, the orientation of the straightline corresponding to the light ray represented by the wavelet isdetermined as a function of the dilation parameter and the orientationparameter and/or the position of the straight line corresponding to thelight ray represented by the wavelet is determined as a function ofthese first and second spatial coordinates.

The invention finally proposes, here again independently, a method forconstructing a depth map related to a scene represented by a digitalhologram, the depth being defined in a given direction of space (here,the three-dimensional space containing the scene), the method comprisingthe following steps:

-   -   reconstructing, by means of the digital hologram, the light        field at a plurality of points in space;    -   for each of a plurality of depths, segmenting the points        associated with the depth concerned into a plurality of        segments, and determining values of a sharpness metric        respectively associated with said segments on the basis of the        light field reconstructed on the segment concerned (that is to        say on the basis of the reconstructed light field values        relative to the points of the segment concerned);    -   for each element of the depth map, determining the depth for        which the sharpness metric is maximum among a set of segments        aligned along said given direction and respectively associated        with the different depths of the plurality of depths, and        associating the so-determined depth with this element.

When the digital hologram is represented by coefficients respectivelyassociated with wavelets, the light field reconstruction is made bymeans of these coefficients.

Of course, the different features, alternatives and embodiments of theinvention can be associated with each other according to variouscombinations, insofar as they are not mutually incompatible orexclusive.

SUMMARY OF THE INVENTION

Moreover, various other features of the invention will be apparent fromthe appended description made with reference to the drawings thatillustrate non-limitative embodiments of the invention, and wherein:

FIG. 1 illustrates an encoding device according to an exemplaryembodiment of the invention;

FIG. 2 illustrates steps of an encoding method in accordance with theteachings of the invention;

FIG. 3 illustrates the relative positioning of a digital hologram and ofthe scene that is represented by this digital hologram;

FIG. 4 schematically shows the calculation of the residuals during theencoding; and

FIG. 5 illustrates steps of a method for constructing a depth map from adigital hologram.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The encoding device 1 of FIG. 1 comprises a processor 2 and a storagedevice 4 (such as a hard drive or a memory). The encoding device 1 canalso comprise a communication circuit 6 allowing the processor 2 toexchange data with an external electronic device (not shown).

The storage device 4 stores at least two digital holograms H₁, H₂ (eachrepresented by a set of coefficients, as explained hereinafter)belonging to a digital hologram sequence (this sequence being intendedto reproduce the evolution over time of a given three-dimensionalscene).

In the example described herein, the storage device 4 further stores athree-dimensional representation S₁; S₂ of the three-dimensional scenerepresented by each of the digital holograms H₁, H₂. However, as analternative, no three-dimensional representation of the scene could bepresent within the encoding device 1. This is in particular the casewhen the digital holograms H₁, H₂ are received by the encoding device 1,via the communication circuit 6.

Indeed, the digital holograms H₁, H₂ can in practice be constructed(previously to the encoding method described hereinafter) within theencoding device 1 on the basis of the three-dimensional representationsS₁, S₂ (as described, for example, in the above-mentioned article“View-dependent compression of digital hologram based on matchingpursuit”), or be received from an external electronic device.

The storage device 4 also stores computer program instructions designedto implement a method as described hereinafter with reference to FIG. 2when these instructions are executed by the processor 2.

In the following of the description, the context considered is thatshown in FIG. 3: using a reference system (O, x, y, z), the digitalholograms H₁, H₂ are defined in the plane of equation z=0.

The digital holograms H₁, H₂ are here respectively represented by twosets of real coefficients c₁(k,s,X), c₂(k,s,X), each coefficientc₁(k,s,X), c₂(k,s,X) being associated with a Gabor-Morlet waveletΨ_(k,s,X) defined by the parameters k, s, X, where

-   -   k is a parameter (integer) that defines the wavelet orientation        θ_(k), with θ_(k)=2πk/N (k varying between 0 and N−1);    -   s is a parameter (integer) that defines the spatial frequency        dilation (s varying between 1 and a);    -   X is a couple of integers that define respectively the        two-dimensional spatial coordinates in the plane of the digital        hologram (that is to say the plane (O, x, y) in FIG. 3), with        X∈[0,N_(x)[x[0,N_(y)[.

The values N, a, N_(x) and N_(y) are fixed for the representationconsidered.

In other words, each Gabor-Morlet wavelet Ψ_(k,s,X) is defined by amultiplet of coordinates k, s, X in a multidimensional space (here,four-dimensional).

Hereinafter, the coefficients c₁(k,s,X) representing the digitalhologram H₁ will be called “first coefficients” and the coefficientsc₂(k,s,X) representing the digital hologram H₂ will be called “secondcoefficients”.

The first and second component of X will be respectively denoted X_(x)and X_(y).

The digital holograms H₁, H₂ could thus be reconstructed as follows:

H₁ = Σ_(k, s,) × c₁(k, s, X) ⋅ Ψ_(k, s, X)H₂ = Σ_(k, s,) × c₁(k, s, X) ⋅ Ψ_(k, s, X)

(the summing being made for all the integers k between 0 and N−1, forall the integers s between 1 and a and for all the couples X of integersin [0,N_(x)[x[0,N_(y)[),

with Ψ_(k,s,X) the function defined by Ψ_(k,s,Z)(Y)=1/s·Φ(R_(k)⁻¹[(Y−ηx)/(s·Δ_(s))]) for Y∈R²,

where η_(x)=(X_(X)·Δ_(x), X_(y)·Δ_(y)), Δ_(x) and Δ_(y) and Δ_(s) denotediscretization pitches of, respectively, the first spatial component inthe plane of the hologram, the second spatial component in the plane ofthe hologram and the spatial frequency dilation,Φ(A)=exp(|A|²/2)·exp(2iπA_(x)f) for A∈R²,

where |A| and Δ_(x) respectively denote the norm (or module) of A andthe first component thereof, exp is the exponential function(exp(p)=e^(ρ)), f is a parameter (predefined for the representationconcerned) and

$R_{k} = {\begin{pmatrix}{\cos\left( \frac{2\pi k}{N} \right)} & {- {\sin\left( \frac{2\pi k}{N} \right)}} \\{\sin\left( \frac{2\pi k}{N} \right)} & {\cos\left( \frac{2\pi k}{N} \right)}\end{pmatrix}.}$

An example of encoding method in accordance with the invention will nowbe described with reference to FIG. 2. This method is aimed at adifferential encoding of the digital hologram H₂ on the basis of thedigital hologram H₁. In this differential encoding, the digital hologramH₁ is used as the reference digital hologram.

This method here starts by a step E2 of segmenting the coefficients intosets of coefficients E_(i) respectively associated with parts P_(i) ofthe scene (which amounts to grouping the wavelets Ψ_(k,s,X) into groupsof wavelets respectively associated with these parts P_(i) of thescene).

Each part P_(i) of the scene is formed by a set of points of a sameregion liable to have a similar movement. Such a part P_(i) of the sceneis hereinafter called “connected component”. In practice, it is forexample an object of the scene.

In the example described herein, the connected components P_(i) are forexample identified on the basis of the three-dimensional representationS₁ of the scene (three-dimensional representation corresponding to thedigital hologram H₁).

As an alternative, the connected components P_(i) can be reconstructedfrom a digital hologram (here H₁), for example by means of a depth map,as described hereinafter.

In step E2, for each coefficient c₁(k,s,X) of the digital hologram H₁,it is determined which part P_(i) (or connected component) of the sceneis passed through by a straight line Δ (representing a light rayassociated with the wavelet Ψ_(k,s,X)) passing through the point ofcoordinates X (in the plane of the digital hologram) and oriented alongthe direction vector V_(k,s) of coordinates:

(cos[θ_(k)]·sin[φs],sin[θ_(k)]·sin[φ_(s)],cos[φ_(s)]),

with φ_(s)=arcsin(λf/(s·Δs)) (where λ is the reference wavelength of thedigital hologram).

The coefficient c₁(k,s,X) is then placed in the set E_(i) associatedwith the part P_(i) passed through by this straight line Δ.

Hence, a plurality of sets E_(i) is constructed, each set E_(i)comprising coefficients c₁(k,s,X) associated with wavelets Ψ_(k,s,X)that model light rays having an intersection with the part P_(i)associated with the set E_(i) concerned. In other words, each set E_(i)corresponds to a group of wavelets Ψ_(k,s,X) that model light rayshaving an intersection with the part P_(i) associated with the set E_(i)concerned.

In certain embodiments (for example, when the scene contains a singleobject, i.e. a single connected component P₁), the segmentation step E2could be omitted. It is considered in this case hereinafter that asingle set E_(i) of coefficients (herein the set E₁) is processed.

The method of FIG. 2 continues with a step E4, in which a rigidtransform F_(i) is determined for each connected component (or part)P_(i) of the scene.

This rigid transform F_(i) is for example determined by analyzing themovement of the connected component P_(i) between the scene representedby the hologram H₁ and the scene represented by the hologram H₂.

This movement analysis is for example made by comparing thethree-dimensional representation S₁ (scene represented by the digitalhologram H₁) and the three-dimensional representation S₂ (scenerepresented by the digital hologram H₂). On this subject, reference willbe made for example to the article “A Hierarchical Method for 3D RigidMotion Estimation”, by Srinark T., Kambhamettu C., Stone M. in ComputerVision—ACCV 2006. ACCV 2006 Lecture Notes in Computer Science, vol 3852.Springer, Berlin, Heidelberg.

As an alternative, this movement analysis could be made by comparing afirst depth map derived (as explained hereinafter) from the digitalhologram H₁ and a second depth map derived (as explained hereinafter)from the digital hologram H₂. Such depth maps allow coming down to theabove-mentioned three-dimensional case.

For each connected component P_(i), the rigid transform F_(i) isclassically decomposed into a translation t^(i)=(t^(i) _(x), t^(i) _(y),t^(i) _(z)) and a rotation r^(i) that can be written (using the Eulerangles) in matrix form, by means of the three following matrices:

$R_{x}^{i} = \begin{pmatrix}1 & 0 & 0 \\0 & {\cos\alpha_{i}} & {{- \sin}\alpha_{i}} \\0 & {\sin\alpha_{i}} & {\cos\alpha_{i}}\end{pmatrix}$ $R_{y}^{i} = \begin{pmatrix}{\cos\beta_{i}} & 0 & {\sin\beta_{i}} \\0 & 1 & 0 \\{{- \sin}\beta_{i}} & 0 & {\cos\beta_{i}}\end{pmatrix}$ $R_{z}^{i} = \begin{pmatrix}{\cos\gamma_{i}} & {{- \sin}\gamma_{i}} & 0 \\{\sin\gamma_{i}} & {\cos\gamma_{i}} & 0 \\0 & 0 & 1\end{pmatrix}$

The method of FIG. 2 then comprises a step E6 of determining, for eachset E_(i) of coefficients, a linear transform T_(i) of thespace-frequency domain on the basis of the rigid transform determined atstep E4 for the connected component P_(i) associated with the set E_(i)concerned.

In the example described herein, the linear transform T_(i) is definedas follows (on the basis of the corresponding rigid transform F_(i)):

$\Omega_{i} = \begin{pmatrix}{\cos\gamma_{i}} & {{- \sin}\gamma_{i}} & 0 & 0 \\{\sin\gamma_{i}} & {\cos\gamma_{i}} & 0 & 0 \\0 & 0 & {\cos\gamma_{i}} & {{- \sin}\gamma_{i}} \\0 & 0 & {\sin\gamma_{i}} & {\cos\gamma_{i}}\end{pmatrix}$ $\tau_{i} = \begin{pmatrix}I_{2} & {\frac{2t_{z}^{i}}{\lambda}I_{2}} \\0 & I_{2}\end{pmatrix}$ $b_{i} = \begin{pmatrix}t_{x}^{i} \\t_{y}^{i} \\\alpha_{i} \\\beta_{i}\end{pmatrix}$ T_(i) : ℝ⁴ → ℝ⁴, w ↦ Ω_(i)τ_(i)w + b_(i)

where λ is the already mentioned reference wavelength and l₂ theidentity matrix with 2 rows and 2 columns.

The method of FIG. 2 then comprises, at step E8, constructing apredicted digital hologram H_(p) as a function of the digital hologramH₁ and by means of the linear transforms Ti determined at step E6.

For that purpose, for each coefficient c₁(k,s,X) associated with awavelet Ψ_(k,s,X) defined by the multiplet (k,s,X) within the digitalhologram H₁, it is determined to which wavelet Ψ_(k′,s′,X′) applies thiscoefficient c₁(k,s,X) within the predicted hologram H_(p) by means ofthe transform T_(i) associated with the set E_(i) containing thiscoefficient c₁(k,s,X):

Considering Σ₁=f·[cos(θ_(k))]/(s·Δ_(s)), ξ₂=f·[sin(θ_(k))]/(s·Δ_(s)) andη=(η_(x),η_(y))=(X_(x)·Δ_(x), X_(y)·Δ_(y)), we calculate

$\begin{pmatrix}\eta^{\prime} \\\xi_{1}^{\prime} \\\xi_{2}^{\prime}\end{pmatrix} = {T_{i}\left\lbrack \begin{pmatrix}\eta \\\xi_{1} \\\xi_{2}\end{pmatrix} \right\rbrack}$

and, considering θ′=atan 2(ξ₁, ξ₂), then:

k′=ent(Nθ′/2π), where ent is the function “integer part”,s′=ent(f/[SQRT(ξ′₁ ²+ξ′₂ ²)·Δ_(s))]) and X′=(ent(η′_(x)/Δ_(x)),ent(η′_(y)/Δ_(y)),

with η′=(η′_(x), η′_(y)).

In other words, for each set E_(i) of coefficients, it is defined (asjust indicated), using the transform T_(i) associated with this setE_(i), a transform G_(i) in the multidimensional space (herefour-dimensional) such that a coefficient c₁(k,s,X) belonging to the setE_(i) and applied to the wavelet Ψ_(k,s,X) in the digital hologram H₁ isapplied to the wavelet Ψ_(Gi(k,s,X)) in the predicted digital hologramH_(p), as schematically illustrated in FIG. 4. (We hence have:(k′,s′,X′)=G_(i)(k,s,X).)

This transform G_(i) is thus the transform that corresponds, in themultidimensional space of the wavelet definition coordinates, to therigid transform F_(i) of the connected component P_(i). This lineartransform Gi is valid for the coefficients of the set E_(i) associatedwith this connected component P_(i).

The predicted digital hologram H_(p) can thus be written:

H_(p) = Σ_(k, s,) × c₁(k, s, X) ⋅ Ψ_(Gi(k, s, X))

In this summing, no account will be taken of the coefficients c₁(k,s,X)for which the image G_(i)(k,s,X) is out of the domain of the values usedin the representation concerned, that is to say, here, out of thefollowing part of the multidimensional space:[0,N−1]x[1,a]x[O,N_(x)[x[O,N_(y)[. These coefficients indeed correspondto rays that exit from the digital hologram frame.

The method of FIG. 2 then comprises a step E10 of determining a set ofresiduals by difference between the digital hologram H₂ (the digitalhologram to be encoded) and the digital hologram H_(p) predicted on thebasis of the digital hologram H₁ (reference digital hologram).

Precisely, for each coefficient c₂(k′,s′,X′) of the digital hologram H₂(this coefficient being relative to a wavelet Ψ_(k′,s′,X′) defined bythe multiplet (k′,s′,X′)), it is determined a residual I_(k′,s′,X′) bydifference between this coefficient c₂(k′,s′,X′) and the coefficientrelative to the same wavelet Ψ_(k′,s′,X′) in the predicted digitalhologram H_(p), i.e. c₁(k,s,X), as illustrated in FIG. 4, with(k′,s′,X′)=G_(i)(k,s,X) as already indicated. We hence have:

I_(k^(′), s^(′), X^(′)) = c₂(k^(′), s^(′), X^(′)) − c₁(k, s, X).

Each residual is hence determined by difference between a coefficientc₂(k′,s′,X′), associated (in the digital hologram H₂) with the waveletΨ_(k′,s′,X′) defined by the multiplet (k′,s′,X′), and a coefficientc₁(k,s,X) associated, in the digital hologram H₁, to a wavelet Ψ_(k,s,X)defined by a multiplet (k,s,X) having for image the multiplet (k′,s′,X′)by the transform G_(i) associated with the set E_(i) comprising thecoefficient c₁(k,s,X).

The method of FIG. 2 finally comprises a step E12 of encoding theresiduals I_(k′,s′,X′).

For example, this can be done as follows:

-   -   ordering the residuals I_(k′,s′,X′) in a predetermined order of        the multiplets (k′,s′,X′);    -   entropy encoding to the ordered residuals using a method of the        Huffman encoding or arithmetic encoding type.

In the just described example, the differential encoding of the digitalhologram H₂ is made with reference to a single digital hologram H₁. Asan alternative, it could be provided to encode the digital hologram H₂with reference to two digital holograms respectively located before andafter the digital hologram H₂ in the digital hologram sequence.

In this case, the value of the bidirectionally predicted coefficientscan be equal to the mean of the coefficients predicted from said twodigital holograms.

For example, if H₃ denotes a digital hologram posterior to the digitalhologram H₂ in the digital hologram sequence and c₃ the coefficients ofthis digital hologram H₃, the residual will be defined by:

I_(k^(′), s^(′), X^(′)) = c₂(k^(′), s^(′), X^(′)) − (c₁(k, s, X) + c₃(k^(″), s^(″), X^(″)))/2,

where, as previously, (k′,s′,X′)=G_(i)(k,s,X) and where(k′,s′,X′)=G′_(i)(k″,s″,X″), with G′_(i) a transform defined similarlyto the transform G_(i), but this time on the basis of a rigid transformF′_(i) determined as a function of the evolution of a connectedcomponent P_(i) of the scene represented by the digital hologram H₃ tothe scene represented by the digital hologram H₂.

FIG. 5 illustrates steps of a method for constructing a depth map from adigital hologram H (as already indicated, this method can be applied tothe hologram H₁ and/or to the hologram H₂).

The depth is here understood in the direction (Oz).

Let's denote M_(x) and M_(y) the horizontal and vertical resolutionsdesired for the depth map, and M_(z) the number of levels of the depthmap.

Let's finally denote z_(min) and z_(max) the minimum and maximum valuesof the z coordinate in the scene (these values being predefined).

The method of FIG. 5 starts with a step E20 in which a variable d isinitialized to the value 0.

The method then comprises a step E22 of reconstructing the light field Uat the depth z_(d)=d·(z_(max)−z_(min))/M_(z)+z_(min), for example usingthe propagation of the angular spectrum:

U = F⁻¹{F(H).exp (2πiz_(d).SQRT[λ⁻² − f_(x)² − f_(y)²])},

where SQRT is the square root function, F and F⁻¹ are respectively thedirect and inverse Fourier transforms, and f_(x) and f_(y) are thefrequency coordinates of the hologram in the Fourier domain.

The method then comprises a step E24 of segmenting the reconstructedfield U into M_(x)·M_(y) segments (rectangular), each segment having ahorizontal resolution K_(x) and a vertical resolution K_(y). (The fieldreconstructed thanks to the hologram H at a horizontal resolution N_(x)and a vertical resolution N_(y), as already indicated, and we have thus:M_(x)·K_(x)=N_(x) et M_(y)·K_(y)=N_(y).)

The method then comprises a step E26 of calculating a sharpness metric vfor each of the segments obtained at step E24. If each segment isindexed by a horizontal index i and a vertical index j, the valuev[i,j,d] of the sharpness metric is calculated for each segment ofindices i, j, here by means of the normalized variance:

v[i, j, d] = (1/M_(x), M_(y).µ[i, j]).∑_(n, m)(❘U[i.K_(x) + n, j.K_(y) + m]❘² − µ[i, j])²

where is the mean intensity of the field of the segment concerned:

µ[i, j] = (1/M_(x).M_(y)).∑_(n, m)❘U[i.K_(x) + n, j.K_(y) + m]❘².

As an alternative, another sharpness metric can be used, for example oneof the metrics mentioned in the article “Comparative analysis ofautofocus functions in digital in-line phase-shifting holography”, by E.S. R. Fonseca, P. T. Fiadeiro, M. Pereira, and A. Pinheiro in Appl.Opt., AO, vol. 55, no. 27, pp. 7663-7674, Sep. 2016.

(Such a sharpness metric calculation is performed for all the segments,i.e. for any i between 0 et M_(x)−1 and for any j between 0 andM_(y)−1.)

The processing related to the depth z_(d) associated with the currentvariable d is then finished.

The method then comprises a step E28 of incrementing the variable d anda step E30 of testing the equality between the current value of thevariable d and the number M_(z) of levels of the depth map.

In case of equality (arrow P), all the levels have been processed andthe method continues at step E32 described hereinafter.

In the absence of equality, at step E30 (arrow N), the method loops tostep E22 for processing the depth level z_(d) corresponding to the (new)current value of the variable d.

The method can then construct, at step E32, the depth map D by choosing,for each element of the map (here indexed by the indices i, j), thedepth (here denoted D[i,j]) for which the sharpness metric is maximum(among the different segments aligned along the axis Oz, here all ofindices i, j, and respectively associated with the different depths ford varying from 0 to M_(z)−1). With the notations already used, we have:

D[i, j] = argmax_(d)v[i, j, d].

A depth value D[i,j] is hence obtained for all the elements of the depthmap D, i.e. here for any i between 0 and M_(x)−1 and for any j between 0and M_(y)−1.

The so-obtained depth map D can be used, as already mentioned, todetermine the connected components (or parts) P_(i) of the scene, forexample by means of a partitioning algorithm (or “clusteringalgorithm”).

A k-means algorithm can be used for that purpose, as described forexample in the article “Some methods for classification and analysis ofmultivariate observations”, by MacQueen, J. in Proceedings of the FifthBerkeley Symposium on Mathematical Statistics and Probability, Volume 1:Statistics, 281-297, University of California Press, Berkeley, Calif.,1967.

In this case, the partitioning algorithm makes it possible to group theconnected segments (here of indices i, j) of close depth values (hereD[i,j]), the so-produced groups forming the connected components P_(i).

1. A method for encoding a sequence comprising at least a first digitalhologram representing a first scene and a second digital hologramrepresenting a second scene, the first digital hologram and the seconddigital hologram being represented by a set of wavelets, each of thewavelets being defined by a multiplet of coordinates in amultidimensional space, the first hologram being represented by a set offirst coefficients respectively associated with at least certain of thewavelets of said set of wavelets and the second hologram beingrepresented by a set of second coefficients respectively associated withat least certain of the wavelets of said set of wavelets, the encodingmethod comprising the following steps: for each given one of a pluralityof the second coefficients, determining a residual as a differencebetween the given second coefficient, associated with a first saidwavelet defined by a given said multiplet, and the first coefficientassociated with a second said wavelet defined by a said multiplet havingfor image the given said multiplet by a transform in themultidimensional space; and encoding the determined residuals, whereinthe transform is determined by analysis of variation between the firstscene represented by the first digital hologram and the second scenerepresented by the second digital hologram.
 2. The method according toclaim 1, wherein said variation corresponds to movement of an objectbetween the first scene and the second scene.
 3. The method according toclaim 1, further comprising, for at least one given said secondcoefficient outside of said plurality of the second coefficients, a stepof determining a residual as a difference between the given said secondcoefficient, associated with a third said wavelet defined by anothergiven said multiplet, and the first coefficient associated with a fourthsaid wavelet defined by another said multiplet having for image saidanother given multiplet by another transform in the multidimensionalspace.
 4. The method according to claim 3, wherein said anothertransform is determined by analysis of another variation between thefirst scene and the second scene.
 5. The method according to claim 3,further comprising the following steps: distributing at least a part ofthe wavelets into different groups of said wavelets respectivelyassociated with different parts of the first scene or the second scene;determining a transform of the multidimensional space for each saidgroup of the wavelets; for each given one of the second coefficients ofa given said group of the wavelets, determining a residual as adifference between the given said second coefficient, associated with afifth said wavelet defined by a given said multiplet, and the firstcoefficient associated with a sixth said wavelet defined by a saidmultiplet having for image this given multiplet by the transformassociated with the given group of the wavelets.
 6. The method accordingto claim 1, wherein the transform is determined as a function of amovement, between the first scene and the second scene, of a set ofconnected points.
 7. The method according to claim 1, wherein thetransform is determined on the basis of three-dimensionalrepresentations of the first scene and the second scene.
 8. The methodaccording to claim 1, further comprising the following steps:constructing a first depth map by means of the first digital hologram;constructing a second depth map by means of the second digital hologram;determining the transform on the basis of the first depth map and thesecond depth map.
 9. The method according to claim 8, wherein, depthbeing defined along a given direction, the step of constructing thefirst depth map comprises the following steps: reconstructing, by meansof the first digital hologram, a light field at a plurality of points;for each given one of a plurality of depths, segmenting those of theplurality of points that are associated with the given depth into aplurality of segments, and determining values of a sharpness metricrespectively associated with said segments on the basis of the lightfield reconstructed on a respective said segment; for each element ofthe first depth map, determining a depth for which the sharpness metricis maximum among a set of the segments aligned along said givendirection and respectively associated with depths of the plurality ofdepths.
 10. The method according to claim 1, wherein the coordinates ofsaid multidimensional space represent respectively a parameterrepresentative of a first spatial coordinate in a plane of the hologram,a parameter representative of a second spatial coordinate in the planeof the hologram, a spatial frequency dilation parameter (s) and anorientation parameter.
 11. A device for encoding a sequence comprisingat least a first digital hologram representing a first scene and asecond digital hologram representing a second scene, the first digitalhologram and the second digital hologram being represented by means of aset of wavelets, each of the wavelets being defined by a multiplet ofcoordinates in a multidimensional space, the encoding device comprising:a unit for storing a set of first coefficients, respectively associatedwith at least certain of the wavelets of said set of wavelets, and a setof second coefficients, respectively associated with at least certain ofthe wavelets of said set of wavelets, the set of first coefficientsrepresenting the first digital hologram and the set of secondcoefficients representing the second digital hologram; a unit fordetermining, for each given one of a plurality of the secondcoefficients, a residual as a difference between the given secondcoefficient, associated with a first said wavelet defined by a givensaid multiplet, and the first coefficient associated with a second saidwavelet defined by a said multiplet having for image the given saidmultiplet by a transform in the multidimensional space; and a unit forencoding the determined residuals, wherein the unit for determining isdesigned to determine the transform by analysis of variation between thefirst scene represented by the first digital hologram and the secondscene represented by the second digital hologram.
 12. The deviceaccording to claim 11, wherein said variation corresponds to movement ofan object between the first scene and the second scene.
 13. The methodaccording to claim 2, further comprising, for at least one given saidsecond coefficient outside of said plurality of the second coefficients,a step of determining a residual as a difference between the given saidsecond coefficient, associated with a third said wavelet defined byanother given said multiplet, and the first coefficient associated witha fourth said wavelet defined by another said multiplet having for imagesaid another given multiplet by another transform in themultidimensional space.
 14. The method according to claim 4, furthercomprising the following steps: distributing at least a part of thewavelets into different groups of said wavelets respectively associatedwith different parts of the first scene or the second scene; determininga transform of the multidimensional space for each said group of thewavelets; for each given one of the second coefficients of a given saidgroup of the wavelets, determining a residual as a difference betweenthe given said second coefficient, associated with a fifth said waveletdefined by a given said multiplet, and the first coefficient associatedwith a sixth said wavelet defined by a said multiplet having for imagethis given multiplet by the transform associated with the given group ofthe wavelets.
 15. The method according to claim 2, wherein the transformis determined as a function of a movement, between the first scene andthe second scene, of a set of connected points.
 16. The method accordingto claim 3, wherein the transform is determined as a function of amovement, between the first scene and the second scene, of a set ofconnected points.
 17. The method according to claim 4, wherein thetransform is determined as a function of a movement, between the firstscene and the second scene, of a set of connected points.
 18. The methodaccording to claim 5, wherein the transform is determined as a functionof a movement, between the first scene and the second scene, of a set ofconnected points.
 19. The method according to claim 2, wherein thetransform is determined on the basis of three-dimensionalrepresentations of the first scene and the second scene.
 20. The methodaccording to claim 3, wherein the transform is determined on the basisof three-dimensional representations of the first scene and the secondscene.